The fare rules refer to "surface segment", not "open jaw"

On one trip I had two surface segments in my continent of origin, which counted as the two allowed stopovers.
Ticketed by AA without any issues being raised.

FYI my Itinerary, in part, was:
KRT-xAMM-JFK... round-the-world...HKG-DME surface to LED-TXL surface to BUD-xLHR-DXB
So in the continent of origin (Europe-Middle East) we touched 8 places!
(KRT, AMM, DME, LED, TXL, BUD, LHR, DXB)

After ticketing there was a schedule change which turned the transit in AMM into a stopover, so we got to see some of the city
In our transit in London, we got in to the city and had an excellent lunch with my sister